Giselle works as a carpenter and as a blacksmith.
She earns
$
20
$20dollar sign, 20 per hour as a carpenter and
$
25
$25dollar sign, 25 per hour as a blacksmith. Last week, Giselle worked both jobs for a total of
30
3030 hours, and earned a total of
$
690
$690dollar sign, 690.
How long did Giselle work as a carpenter last week, and how long did she work as a blacksmith?
Giselle worked as a carpenter for
hours and as a blacksmith for
hours last week.

Answer:

[tex](x-14)^2 +(y-22)^2 = (\sqrt{65})^2[/tex]

Step-by-step explanation:

If the two given points are the extremes of the diameter, the center of the circle has to be its middle point - that we can find by taking the average of the coordinates. The center thus sits in

[tex](\frac{22+6}2; \frac{21+23}2)[/tex] or [tex](14; 22)[/tex]. At this point we either find the length of the diameter and halve it, or the distance between the center and either point. Let's go for the diameter.

[tex]r=\sqrt{(22-6)^2+(21-23)^2}=\sqrt{16^2+2^2} = \sqrt {260}=2\sqrt{65}[/tex]. That makes our radius half of that. We can easily write the equation of the circle now:

[tex](x-14)^2 +(y-22)^2 = (\sqrt{65})^2[/tex]

Now, in theory you can improve it by multiplying it out and taking every term to the LHS, but I think it's good enough like that.

The volume of the triangular prism is V = 18ft³

The volume of the prism is equal to the area of the triangular face, times the length of the prism, which is 9ft.

Remember that the area of a triangle of base B and height H is:

A = B*H/2

Here we can see that the base is 2ft and the height is 2ft, then the area of the triangular face is:

A = 2ft*2ft/2 = 2ft²

And thus, the volume of the prism is:

V = 2ft²*9ft

V = 18ft³

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a. The number of possible access codes. The number of different codes available is 343.

b. The probability of randomly selecting the correct access code on the first try is 0.003

a. To find the number of possible access codes. The number of different codes available is:

= 7* 7* 7

= 343

(b) The probability of randomly selecting the correct access code is nnothingwill be:

P = 1/343

= 0.003

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The access code for a safe consists of three digits. Each digit can be any number from 0 through 6 , and each digit can be repeated. Complete parts (a) through (c). a) Find the number of possible access codes. (b) What is the probability of randomly selecting the correct access code on the first try? (c) What is the probability of not selecting the correct access code on the first try? (a) Find the number of possible access codes. The number of different codes available is nothing . (b) What is the probability of randomly selecting the correct access code on the first try?

The exponential value equation is A = 1/√x = 1/x^(-1/2)

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

A = x ^ ( 1/6 ) / x ^ ( 2/3 )

On simplifying , we get

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

So , A = x ^ ( 1/6 - 2/3 )

On further simplification , we get

A = x ^ ( -3/6 )

A = x ^ ( -1/2 )

So , the value of A is

A = 1/√x

Hence , the exponential equation is solved

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The value of x for each item is given as follows:

28. x = 5.

29. x = 3.44.

For item 28, we apply the crossing chord theorem, which states that the products of the parts of the chords are equal, hence the value of x is obtained as follows:

16x = 10 x 8

16x = 80

x = 5.

For item 29, we apply the two secant theorem, hence the value of x is obtained as follows:

10(x + 10) = 12(12 + 25)

10x + 100 = 444

10x = 344

x = 3.44.

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Answer:

The angle in the first problem measures 67°.

x=16, y=40

Step-by-step explanation:

1st problem: draw the line r in figure (red) parallel to the two given one and containing the vertex of the angle. The two green angles are congruent since alternate angles from the two parallels t and r when crossed with the upper side of the angle. Same with the two blue angles created by the parallels r and b. The measure of the angle you need is the sum of the two, or 36+31= 67°.

Second problem. The two angles in red are congruent since corresponding angles generated by the parallels m and b and the transversal r. we can then write [tex]4x-5=3x+11\\[/tex]. Solving for x we find x= 16. Now the two angles marked in blue are conjugates when looking at the parallels l and r cut by the transversal m, thus they add up to 180° We know how much the angle with double marks measures (since we found x earlier) so we can write

[tex](3y+1) + (4\times16-5) = 180\\3y+ 1 + 59 = 180\\3y=120 \implies y=40[/tex]

The slope of the graph f(x) = (1/3)x + 4 is less than the slope of g(x) = 4x-1

f(x) = 1/3 x + 4

g(x) = 4x - 1

The equation of line is given by y = mx +c

On comparing both equation with y = mx + c

m is the slope of the line and c is the intercept of the equation

Let the slope of f(x) is m₁

In f(x) =1/3 x + 4

m₁ = 1/3 = 0.33

Let the slope of g(x) is m₂

In g(x)  = 4x - 1

m₂ = 4

m₁ < m₂

slope of f(x) is less than slope of g(x)

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   The solution to the system of equations is x = 1,y = -1 by using the elimination method.

  To solve the system of equations using the elimination method, we'll eliminate one variable by adding or subtracting the equations. Here's how:

  Multiply the first equation by 2 to make the coefficients of y in both equations opposite each other:

Equation 1: 2(y + 2x) = 2(1) => 2y + 4x = 2

  Rewrite the second equation as:

Equation 2: 3x - 2y = 5

  Now, we can add the modified Equation 1 to Equation 2 to eliminate y:

(2y + 4x) + (3x - 2y) = 2 + 5

  Simplifying, we get:

4x + 3x = 7

7x = 7

  Divide both sides of the equation by 7 to solve for x:

x = 7/7

x = 1

  Substitute the value of x into either of the original equations. Let's use the first equation:

y + 2(1) = 1

y + 2 = 1

  Subtract two from both sides of the equation to solve for y:

y = 1 - 2

y = -1

  Therefore, the solution to the system of equations is:

x = 1

y = -1

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Answer:

To make a box-and-whisker plot, we first need to order the data from smallest to largest:

4, 5, 6, 10, 15, 16, 21

Next, we can find the median, which is the middle value of the ordered data set. In this case, the median is 10.

Then, we can find the lower quartile (Q1) and the upper quartile (Q3). The lower quartile is the median of the lower half of the data set, and the upper quartile is the median of the upper half of the data set. To find Q1 and Q3, we can split the data set into two halves:

4, 5, 6, 10 and 15, 16, 21

The median of the lower half is (5+6)/2 = 5.5, and the median of the upper half is (16+21)/2 = 18.5. Therefore, Q1 = 5.5 and Q3 = 18.5.

Now we can draw the box-and-whisker plot. The box represents the middle 50% of the data, with the bottom of the box at Q1 (5.5), the top of the box at Q3 (18.5), and the line inside the box at the median (10). The whiskers extend from the box to the smallest and largest values inthe data set that are not outliers. To determine whether there are outliers, we can use the following formula:

Outlier = Q1 - 1.5 * (Q3 - Q1) or Q3 + 1.5 * (Q3 - Q1)

Plugging in the values, we get:

Outlier = 5.5 - 1.5 * (18.5 - 5.5) = -13.25 or Outlier = 18.5 + 1.5 * (18.5 - 5.5) = 37.25

Since there are no values in the data set that are less than -13.25 or greater than 37.25, there are no outliers.

Therefore, the box-and-whisker plot for the given data is:

            |       4

     ___|___

    |              |

    |              |

    |        5.5 |-----  

    |              |      |

    |              |      |

    |------------|  10 |  

    |              |       |

    |      15.5 |------

    |       |      |

     ___|___

            |       21

The box spans from Q1 (5.5) to Q3 (18.5), with the median line inside the box at 10. The whiskers extend from the box to the minimum value of 4 and the maximum value of 21, since there are no outliers.

Hope this helps!

Answer:

The third option

Step-by-step explanation:

Answer:

19.24 ft

Step-by-step explanation:

x = length of ramp

sin12 = 4/x

x = 4/sin12 = 19.24 ft

A number line that shows the solutions to x+8 > 15 include the following: B. number line B.

In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Based on the information provided above, we have the following equation (inequality);

x + 8 > 15

By subtracting 8 from both sides of the equation (inequality), we have;

x + 8 - 8 > 15 - 8

x > 7

This ultimately implies that, the inequality must be shaded to the right with an open dot because the inequality symbol is greater than (>).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Circle Terminology:

Center: The point at the center of the circle.

Radius: The distance from the center to any point on the circle.

Diameter: The distance across the circle passing through the center (2 times the radius).

Chord: A line segment connecting two points on the circle.

Arc: A part of the circumference of the circle.

Sector: The region enclosed by two radii and the corresponding arc.

Circle Formulas:

Circumference (C): C = 2πr or C = πd (where r is the radius and d is the diameter).

Area (A): A = πr^2.

Central Angles and Arcs:

Central Angle: An angle whose vertex is at the center of the circle.

Arc Measure: The measure of the central angle that intercepts the arc.

Arc Length: The distance along the circumference of the circle.

Arc Length = (Arc Measure / 360) * Circumference.

Inscribed Angles and Arcs:

Inscribed Angle: An angle formed by two chords with its vertex on the circle.

Inscribed Angle Theorem: An inscribed angle is half the measure of its intercepted arc.

Intercepted Arc: The arc that lies between the endpoints of the inscribed angle.

Tangents:

Tangent: A line that intersects the circle at exactly one point (the point of tangency).

Tangent Theorem: A tangent line is perpendicular to the radius drawn to the point of tangency.

Secants:

Secant: A line that intersects the circle at two points.

Intersecting Chord Theorem: The product of the lengths of the two segments of a secant is equal to the product of the lengths of its external segment.

Relationships Between Angles and Arcs:

Angle-Arc Relationship: The measure of an inscribed angle is half the measure of its intercepted arc.

Angle in a Semicircle: An angle inscribed in a semicircle is a right angle (90 degrees).

Circle Construction:

Circumscribed Circle: A circle that passes through all the vertices of a polygon.

Incircle: A circle that is tangent to all the sides of a polygon.

Remember to practice solving problems involving these concepts, including finding angles, arc measures, lengths, and areas of circles. Additionally, review the properties and relationships between angles and arcs in different scenarios. Good luck with your study and the test!

Answer:

The distance between Garland and Mansfield on the map is 15 inches.

Step-by-step explanation:

On Giana's map of Texas, the scale is 1 inch = 3.5 miles. To determine the distance between Garland and Mansfield on the map, we can use the scale to find the corresponding measurement. Given that the actual distance between these two cities is 52.5 miles, we can set up a proportion:

1 inch / 3.5 miles = x inches / 52.5 miles

Cross-multiplying, we have:

3.5 miles * x inches = 1 inch * 52.5 miles

3.5x = 52.5

Dividing both sides by 3.5, we find:

x = 15

Therefore, the distance between Garland and Mansfield on the map is 15 inches.

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The interior angles of the trapezium is as follows:

The sum of interior angles in a quadrilateral is 360 degrees. Therefore, the diagram above is a trapezium with 4 sides.

Let's find the measure of each interior angles

2x + 2x + 20 + 2x - 10 + 3x - 10 = 360

9x  = 360

divide both sides by 9

x = 360 / 9

x = 40

Therefore, each interior angles is as follows:

2x = 2(40) = 80 degrees

2x + 20 = 2(40) + 20 = 100 degrees

2x - 10 = 2(40) - 10 = 70 degrees

3x - 10 = 3(40) - 10 = 110 degrees

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The value of side TS is,

⇒ TS = 28

First, we are going to divide the figure and named new points X and Y as:

Now, we know that TS is the sum of TX and XS.

TS = TX + XS

Additionally, TX has the same length of HJ, so:

TX = HJ = 14

Now, we want to know the length of YK, and we can calculate it using the following equation:

LK = LY + YK

LY = HJ,

so, LY = 14

And, 42 = 14 + YK

42 - 14 = YK

28 = YK

Finally, since T and S are midpoints, the length of XS is the half of the length of YK. It means that XS is:

XS = YK/2

XS = 28/2

XS = 14

Therefore, TS is equal to:

TS = TX + XS

TS = 14 + 14

TS = 28

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The equation shows that the point total in the 10th level is predicted to be 514.4.

The equation given is: y= 48.2x + 32.4

where y is the point total and x is the level.

In order to predict the point total in the 10th level, I will substitute x=10 into the equation:

y=48.2(10) + 32.4 = 482 + 32.4 = 514.4

Therefore, the point total in the 10th level is predicted to be 514.4.

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Step-by-step explanation:

The volume of a pyramid is 1/3 bh

First step is to find the base

The area of a triangle is 1/2 bh

We have both b and h of the base triangle

Area of base = 16.5 cm^2

Now we can sub. that in with the volume formula

1/3 16.5 x 9

1/3 x 148.5

49.49999999999995

The vector representing the radius at the given position is  -13i - j  - 5k.

The magnitude of the radius vector is 13.96 units.

The vector representing the radius at the given position is calculated as follows;

center of the sphere = (11, 5, 2)

The point of the radius = ( -2, 4, -3 )

The radius vector = ( - 2 - 11) , ( 4 - 5), ( -3 - 2)

r = ( -13, - 1, - 5)

r = -13i - j  - 5k

The magnitude of the radius vector is calculated as follows;

| r | = √ x² + y² + z²

where;

| r | = √[ ( -13²) + ( -1)² + ( -5 )² ]

| r | = √ ( 169 + 1 + 25 )

| r | = √ ( 195 )

| r | = 13.96 units

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The vertices of the image triangle △JKL under the dilation centered at the origin with a scale factor of 5 are:

J′ = (−15, −10)

K′ = (5, 20)

L′ = (20, 10)

To find the vertices of the image of triangle △JKL under the dilation centered at the origin with a scale factor of 5, we need to multiply the coordinates of each vertex by the scale factor.

Let's apply the dilation to each vertex:

J(−3, −2) → J′ [tex]= (5 \times -3, 5 \times -2)[/tex] = (−15, −10)

K(1, 4) → K′ [tex]= (5 \times 1, 5 \times 4)[/tex] = (5, 20)

L(4, 2) → L′ [tex]= (5 \times 4, 5 \times 2)[/tex] = (20, 10)

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The area of the triangle is 6x³y⁵

The space enclosed by the boundary of a plane figure is called its area.

A triangle is a polygon with three sides having three vertices.

There are different types of triangle, scalene triangle, equailteral triangle, isosceles triangle, right triangle e.t.c

The area of a triangle is expressed as ;

A = 1/2 bh

where b is the base and h is the height of the of the triangle.

Base = 3x²y²

height = 4x4y³

A = 1/2 × 3x²y² × 4x4y³

A = 1/2 × 12x³y⁵

A = 6x³y⁵

Therefore the area of the triangle is 6x³y⁵

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The area of the Triangle is [tex]48x^{3} y^{4}[/tex]

Triangle is a two-dimensional  three-sided polygon, which has three vertices, three sides and three angles. It is a shape formed when three straight lines meet.

How to determine this

Area of triangle = 1/2 base * height as given

Where area of triangle = ?

Base = [tex]3x^{2} y2[/tex]

i.e 3 * 2 [tex]x^{2} y[/tex]

Base, b = [tex]6x^{2} y[/tex]

Height = [tex]4x4y^{3}[/tex]

i.e [tex]4x[/tex] * [tex]4y^{3}[/tex]

Height,b = [tex]16xy^{3}[/tex]

Area of triangle = 1/2 * [tex]6x^{2} y[/tex] * [tex]16xy^{3}[/tex]

Area = 1/2 * 96* [tex]x^{2+1}[/tex] * [tex]y^{1+3}[/tex]

Area = 1/2 * 96 * [tex]x^{3}[/tex] * [tex]y^{4}[/tex]

Area = 48 * [tex]x^{3} y^{4}[/tex]

Area of the triangle = [tex]48x^{3} y^{4}[/tex]

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The probability of drawing two yellow marbles is 0.015 to the nearest thousandth.

The probability of drawing two yellow marbles after drawing a yellow marble on the first draw and without replacement drawing another yellow marble is determined as follows:

Total number of marbles in the bag = 4 + 2 + 6

Total number of marbles in the bag = 12 marbles in the bag.

P(Yellow on first draw) = 2/12 or 1/6

P(Yellow on second draw | Yellow on first draw) = 1/11

The probability of both marbles being yellow will be:

P(Both marbles yellow) = (1/6) * (1/11)

P(Both marbles yellow)  = 1/66 or 0.015

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The surface area of the cylinder has a radius of 8cm and a height of 10 cm is 502.4 square centimeters.

We know that,

In geometry, a cylinder is one of the basic 3d shapes with two parallel circular bases at a distance. A curving surface connects the two circular bases at a predetermined distance from the centre. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases. One real-world example of a cylinder is an LPG gas-cylinder.

The surface area of this cylinder is defined as the product of the radius of the base and the height of the cylinder.

The surface area of this cylinder = (2π x r)h

We have given a radius of the base is 8 cm and the height of the cylinder is 10 cm.

The surface area of this cylinder = (2π x r)h

= (2π x 8)10

= (50.24)10

= 502.4

Thus, The surface area of the cylinder has a radius of 8cm and a height of 10 cm is 502.4 square centimeters.

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The complete question is attached below:

Answer:

10

Step-by-step explanation:

300 plus 200 is 500

80 minus 30 is 50

500 divided by 50 is 10

The measure of m∠A in the triangle is:

m∠A = 38.44°

The cosine rule is used for solving triangles which are not right-angled in which two sides and the included angle are given. The following are cosine rule formula for angles:

cos(A) = (b² + c² − a²)/2bc

cos(B) = (c² + a² − b²)/ 2ac

cos(C) = (a² + b² − c²)/2ab

Where a, b and c are the length of the sides, and A, B, and C are the measures of the angles

We have:

a = BC = 20

b = AC = 23

c = AB = 32

Substituting into:

cos(A) = (b² + c² − a²)/2bc

cos(A) = (23² + 32² − 20²)/(2*23*32)

cos(A) = 0.7833

A = cos⁻¹(0.7833)

A = 38.44°

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Answer: 2ˣ =  y

Step-by-step explanation:

In order to find the inverse of any function, switch the x and the y, then solve for y.

y = log₂x               >swap/switch variables  and solve for y

x = log₂y              >rewrite in exponential form

2ˣ =  y

The graph that shows the solution set of the inequality is the second one.

Here we have the following inequality:

y < |x + 3|

Notice that we have the symbol "<", then we know that the graph of the absolute value must be with dashed lines (because the points that lie on the graph aren't solutions).

Also, y is smaller than that, then the shaded region must be below the graph.

With that in mind, we conclude that the correct option is the second one.

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